A small company makes only two products (X and Y), with the following production constraints representing two machines and their maximum availability:
2X + 3Y ≤ 18
2X + Y ≤ 10
X ≥ 0, Y ≥ 0
where: X = units of the first product, Y = units of the second product
If the profit equation is Z = $4X + $2Y, the maximum possible profit is:
A) $20
B) $21
C) $18
D) $24
E) $14

Question

Quizplus · Accepted Answer

The feasible region is a quadrilateral with vertices at (0,0), (0,6), (5,0), and (3,4). The profit function is maximized at the vertex (3,4), where the profit is $4(3) + $2(4) = $20.

A Small Company Makes Only Two Products (X and Y)